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more fixes to pvector tutorial
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content/static/tutorials/pvector/index.html

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@@ -537,16 +537,6 @@ <h5>Vectors: Magnitude</h5>
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<h5>Vectors: Normalizing</h5>
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Calculating the magnitude of a vector is only the beginning. The magnitude function opens the door to many possibilities, the first of which is normalization. Normalizing refers to the process of making something ÒstandardÓ or, well, Ònormal.Ó In the case of vectors, letÕs assume for the moment that a standard vector has a length of one. To normalize a vector, therefore, is to take a vector of any length and, keeping it pointing in the same direction, change its length to one, turning it into what is referred to as a unit vector.
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Being able to quickly access the unit vector is useful since it describes a vectorÕs direction without regard to length, and weÕll see this come in handy once we start to work with forces in Chapter 2.
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For any given vector , its unit vector (written as ž) is calculated as follows:
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<li>ž = / ||||
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Calculating the magnitude of a vector is only the beginning. The magnitude function opens the door to many possibilities, the first of which is <strong><em>normalization</em></strong>. Normalizing refers to the process of making something "standard" or, well, "normal." In the case of vectors, let's assume for the moment that a standard vector has a length of one. To normalize a vector, therefore, is to take a vector of any length and, keeping it pointing in the same direction, change its length to one, turning it into what is referred to as a <strong><em>unit vector</em></strong>.
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<img src="imgs/normalize1.jpg">
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&#251; = <strong>u</strong> / ||<strong>u</strong>||
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In other words, to normalize a vector, simply divide each component by its magnitude. This makes pretty intuitive sense. Say a vector is of length 5. Well, 5 divided by 5 is 1. So looking at our right triangle, we then need to scale the hypotenuse down by dividing by 5. And so in that process the sides shrink, dividing by 5 as well.
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<img src="imgs/normalize2.jpg">

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